pottersheep
Grade 12 math help please!! For what value of b will the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1?
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TAKEBACKMATH
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okay I will show you:
pottersheep
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thank you so much!
pottersheep
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:(
TAKEBACKMATH
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thinking
pottersheep
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oh ok sorry
TAKEBACKMATH
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sorry, it too late for me I will hand this over to lonesome else?
pottersheep
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ok
pottersheep
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thanks anyways
Callisto
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Here it goes~
Have you learnt remainder theorem yet?
Callisto
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@pottersheep Are you there??
pottersheep
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Yes sorry, we have!
Callisto
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So, let R be the remainder when p(x) is divided by x-2. By remainder theorem, what would you get? I mean p(_) = ...?
pottersheep
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ok one sec
pottersheep
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So i'd sub in 2 for x
Callisto
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Yup!
pottersheep
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3?
pottersheep
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sorryryyryryryr
pottersheep
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Sorry what do I do with the b though?
pottersheep
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4b -24
Callisto
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Right, so for p(2), you get p(2) = 4b - 24 = R, agree?
(By remainder theorem, p(a) = R , when p(x) is divided by x-a)
pottersheep
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Right, okay
Callisto
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And what is the remainder when p(x) is divided by x+1 ?
pottersheep
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b - 5
Callisto
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Not really..
Remainder = p(-1) = -2(-1)^3 + b(-1)^2 - 5(-1) +2 = ...?
pottersheep
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Opps, sorry! I subbed in 1!
pottersheep
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9??
pottersheep
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b + 9!
Callisto
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Yes.
Note that the remainder is p(x) = R when p(x) is divided by x-a.
Now, p(x) is divided by x+1, so a = -1 in the case. [ x-(-1) = x+1]
pottersheep
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True, sorry!
Callisto
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From the question, the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1. So, equate the two remainder you got and solve b. Got it?
Callisto
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Oh.. It's okay!
pottersheep
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Ohhhhhhhhh, so make them equal to each other?? Yes I get it, thank you!!!!!!
Callisto
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Yes. Since they have the SAME remainder!
You're welcome :)